Jeudi 14 septembre à 14h00 en salle E302 du bâtiment CPE, Swann Marx (GIPSA Lab-LAGEP) va présenter son travail de thèse. Il soutiendra sa thèse le 20 septembre à Grenoble. Son travail porte principalement sur la stabilisation d’EDPs par commande saturée.

Voila le résumé de sa présentation.

ABSTRACT :
This thesis provides contributions in stabilization methods for nonlinear dynamical systems. In particular, it focuses on two main subjects: the analysis of infinite-dimensional systems subject to saturated inputs and the design of output feedback laws for either infinite-dimensional or finite-dimensional systems.

The presentation will focus on the first subject.

In the first part, we will introduce a more general class of saturations than the one known for finite-dimensional systems. When bounding a linear stabilizing feedback law with such nonlinearity, a well-posedness result together with an attractivity result will be stated for systems whose open-loop is defined by operators generating strongly continuous semigroup of contractions. The attractivity result will be proved by using the LaSalle’s Invariance Principle together with some compactness properties.

In the second part, a particular nonlinear partial differential equation is studied, namely the Korteweg-de Vries equation, that models long waves in water of relatively shallow depth. A control actuating on a small part of the channel will be considered. This control will be modified with two different types of saturations. The attractivity result will be proved by using Lyapunov argument and a contradiction argument. Finally, the results will be illustrated with some numerical simulations.